Problem: What do the following two equations represent? $5x-2y = 2$ $-10x+4y = 5$
Putting the first equation in $y = mx + b$ form gives: $5x-2y = 2$ $-2y = -5x+2$ $y = \dfrac{5}{2}x - 1$ Putting the second equation in $y = mx + b$ form gives: $-10x+4y = 5$ $4y = 10x+5$ $y = \dfrac{5}{2}x + \dfrac{5}{4}$ The slopes are equal, and the y-intercepts are different, so the lines are parallel.